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IKMC 2023 - Grades 11-12 - Set 2 - Self-study Question 21

IKMC · IKMC 2023 - Grades 11-12 - Set 2 - Self-study

Question 21

Two functions $f,g$ on $\mathbb R$ satisfy $f(x)+2g(1-x)=x^2$ and $f(1-x)-g(x)=x^2$ for every real $x$. What is $f$?
  1. $x^2-\frac43x+\frac23$
  2. $x^2+\frac43x+\frac23$
  3. $-x^2-\frac43x+\frac23$
  4. $x^2-4x+5$
  5. There are no such functions